Preheat the oven to 350°F (175°C). Line a 9×9-inch baking dish with parchment paper to minimize sticking and make the finished bars easier to lift from the pan. Set the lined dish aside while preparing the batter.
Place the melted and cooled unsalted butter and firmly packed light brown sugar in a large mixing bowl. Stir until the mixture is smooth and thoroughly blended.
Add the room-temperature eggs, molasses, and vanilla extract. Continue mixing until all of the wet ingredients are evenly incorporated. Using eggs at approximately 70°F helps the ingredients combine more uniformly.
In a separate medium bowl, whisk together the all-purpose flour, ground ginger, ground cinnamon, baking powder, and kosher salt. Continue whisking until the spices, salt, and leavening are evenly dispersed throughout the flour.
Gradually incorporate the dry mixture into the bowl containing the wet ingredients. Stir just until the batter becomes smooth and completely combined, taking care not to overmix.
Transfer the finished batter to the parchment-lined baking dish and spread it into an even layer.
Place the pan in the preheated oven and bake for 30–35 minutes. The brownies are ready when the edges appear set and the center no longer jiggles.
A toothpick inserted into the center should emerge mostly clean when the bars are properly baked.
Allow the gingerbread brownies to cool completely in the baking pan. Once cooled, lift them from the pan and generously dust the surface with confectioners’ sugar.
Slice into squares before serving.